where the infimum is taken over all simply connected domains containing \(\Lambda _{2R}\)  and contained in \(\Lambda _{3n}\) 
and \(\mathbf {M}_r(\mathcal {D},R)\)  is an increasing random variable defined in [1]}.
When \(R \le L(p)\) , Theorem REF  implies that \(\phi _{p}[E] \!{\begin{array}{c}>\\[-10pt]\scriptstyle {\frown }\end{array}}\!1\) .
Moreover, since \(\mathbf {M}_r(\mathcal {D},R)\)  is increasing,
\(\inf _{\mathcal {D}}\phi _{\mathcal {D},p}[ \mathbf {M}_r(\mathcal {D},R)]\ge \inf _{\mathcal {D}}\phi _{\mathcal {D},p_c}[ \mathbf {M}_r(\mathcal {D},R)] \!{\begin{array}{c}>\\[-10pt]\scriptstyle {\frown }\end{array}}\!(R/r)^{\delta _0},\) 
